73,564 research outputs found
Fast ADMM Algorithm for Distributed Optimization with Adaptive Penalty
We propose new methods to speed up convergence of the Alternating Direction
Method of Multipliers (ADMM), a common optimization tool in the context of
large scale and distributed learning. The proposed method accelerates the speed
of convergence by automatically deciding the constraint penalty needed for
parameter consensus in each iteration. In addition, we also propose an
extension of the method that adaptively determines the maximum number of
iterations to update the penalty. We show that this approach effectively leads
to an adaptive, dynamic network topology underlying the distributed
optimization. The utility of the new penalty update schemes is demonstrated on
both synthetic and real data, including a computer vision application of
distributed structure from motion.Comment: 8 pages manuscript, 2 pages appendix, 5 figure
Low-level Vision by Consensus in a Spatial Hierarchy of Regions
We introduce a multi-scale framework for low-level vision, where the goal is
estimating physical scene values from image data---such as depth from stereo
image pairs. The framework uses a dense, overlapping set of image regions at
multiple scales and a "local model," such as a slanted-plane model for stereo
disparity, that is expected to be valid piecewise across the visual field.
Estimation is cast as optimization over a dichotomous mixture of variables,
simultaneously determining which regions are inliers with respect to the local
model (binary variables) and the correct co-ordinates in the local model space
for each inlying region (continuous variables). When the regions are organized
into a multi-scale hierarchy, optimization can occur in an efficient and
parallel architecture, where distributed computational units iteratively
perform calculations and share information through sparse connections between
parents and children. The framework performs well on a standard benchmark for
binocular stereo, and it produces a distributional scene representation that is
appropriate for combining with higher-level reasoning and other low-level cues.Comment: Accepted to CVPR 2015. Project page:
http://www.ttic.edu/chakrabarti/consensus
Long-distance entanglement and quantum teleportation in XX spin chains
Isotropic XX models of one-dimensional spin-1/2 chains are investigated with
the aim to elucidate the formal structure and the physical properties that
allow these systems to act as channels for long-distance, high-fidelity quantum
teleportation. We introduce two types of models: I) open, dimerized XX chains,
and II) open XX chains with small end bonds. For both models we obtain the
exact expressions for the end-to-end correlations and the scaling of the energy
gap with the length of the chain. We determine the end-to-end concurrence and
show that model I) supports true long-distance entanglement at zero
temperature, while model II) supports {\it ``quasi long-distance''}
entanglement that slowly falls off with the size of the chain. Due to the
different scalings of the gaps, respectively exponential for model I) and
algebraic in model II), we demonstrate that the latter allows for efficient
qubit teleportation with high fidelity in sufficiently long chains even at
moderately low temperatures.Comment: 9 pages, 6 figure
Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions
A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy
- …